1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
-BARSIC- [3]
3 years ago
13

A nonzero polynomial with rational coefficients has all of the numbers [1 sqrt{2}, ; 2 sqrt{3}, ;3 sqrt{4},; dots, ;1000 sqrt{10

01}]as roots. What is the smallest possible degree of such a polynomial?
Mathematics
1 answer:
Colt1911 [192]3 years ago
8 0

Answer:

Its degree can be at least 1970

Step-by-step explanation:

for each root of the form √q, where q is not a square, we have a root -√q. Therefore, we need to find, among the numbers below to 1000, how many sqaures there are.

Since √1000 = 31.6, we have a total of 30 squares:

2², 3², 4², ...., 30², 31²

Each square gives one root and the non squares (there are 1000-30 = 970 of them) gives 2 roots (one for them and one for the opposite). Hence the smallest degree a rational polynomial can have is

970*2 + 30 = 1970

You might be interested in
I need help please thanks​
svet-max [94.6K]

Answer: You simply need to match each fraction to where they belong

Step-by-step explanation:

3 0
3 years ago
Find the average rate of change of each function over the interval [0, 2]. Match each representation with its respective average
marishachu [46]
Average rate of change over interval [a,b]: r=[f(b)-f(a)]/(b-a)
In this case the interval is [0,2], then a=0, b=2
r=[f(2)-f(0)]/(2-0)
r=[f(2)-f(0)]/2

1) First function: h(x)
r=[h(2)-h(0)]/2
x=2→h(2)=(2)^2+2(2)-6
h(2)=4+4-6
h(2)=2
x=0→h(0)=(0)^2+2(0)-6
h(0)=0+0-6
h(0)=-6
r=[h(2)-h(0)]/2
r=[2-(-6)]/2
r=(2+6)/2
r=(8)/2
r=4

2) Second function: f(x)
A function, f, has an
x-intercept at (2,0)→x=2, f(2)=0
and a y-intercept at (0,-10)→x=0, f(0)=-10
r=[f(2)-f(0)]/2
r=[0-(-10)]/2
r=(0+10)/2
r=(10)/2
r=5

3) Third function: g(x)
r=[g(2)-g(0)]/2
From the graph:
g(2)=6
g(0)=2
r=(6-2)/2
r=(4)/2
r=2

4) Fourth function: j(x)
r=[j(2)-j(0)]/2
From the table:
x=2→j(2)=-8
x=0→j(0)=4
r=(-8-4)/2
r=(-12)/2
r=-6

Answer:
Pairs
1) h(x)     4
2) f(x)      5
3) g(x)     2
4) j(x)     -6
8 0
4 years ago
За +6+5а<br> Can you write an equivalent expression by combining like terms.
Alexxx [7]

Answer:

It's 8a + 6

Plz mark brainiest thx

4 0
3 years ago
How to put 1760 into a fraction
Nikolay [14]
Is there a decimal, if so i can answer.
7 0
3 years ago
Read 2 more answers
your friend is Graphing the point (5,3) the first step is to start at the organ and go 5 spaces. which statement about his metho
Lena [83]

Answer:

Moving 5 spaces

Step-by-step explanation:

Although your friend is correct in moving 5 spaces, they don't specify which direction they move in. They could be moving left, right, up, or down.

6 0
3 years ago
Other questions:
  • We want to place a bench measuring 7.05 feet in the center of a platform that is 40.75 feet long. What is the distance from each
    6·1 answer
  • If two sides of a triangle are 1 and 3, the third side may be?
    9·1 answer
  • What are the zeros of the quadratic function f(x) = 2x2 + 16x – 9?
    6·1 answer
  • A recipe for sparkling grape juice calls for 112 quarts of sparkling water and 34 quart of grape juice. How much of each ingredi
    15·1 answer
  • 1. Circle the figure you would use to make the Escher‐like tessellation given.
    7·2 answers
  • An item that originally costs $12.00 was on the clearance aisle for $3.60. What is the percentage of discount?
    6·1 answer
  • The sum of a certain number and -3.4 is -8.1 find the number​
    7·2 answers
  • Proportional quantities are always in the same _______________.
    13·1 answer
  • Please help me thank you
    5·1 answer
  • Given g(x)=-4x+4g(x)=−4x+4, find g(3)
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!